M 9.0 mainshock triggered by diffusional propagation of 7.3 foreshock w

LETTER
Earth Planets Space, 63, 767–771, 2011
Possibility of Mw 9.0 mainshock triggered by diffusional propagation of
after-slip from Mw 7.3 foreshock
Ryosuke Ando and Kazutoshi Imanishi
Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology,
Cetral 7, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8567, Japan
(Received April 7, 2011; Revised May 17, 2011; Accepted May 18, 2011; Online published September 27, 2011)
For the 2011 off the Pacific coast of Tohoku, Japan, Earthquake, we have investigated the spatio-temporal
changes in seismicity from the Mw 7.3 foreshock, March 9, 2011, 11:45, to the Mw 9.0 mainshock, March 11,
14:46 (Japan Standard Time). We found that seismic activities slowly migrated from the source area of the
foreshock, which presumably reflected the propagation of the after-slip. The mainshock rupture was initiated
when the migration reached the hypocentral location of the mainshock. We also found that the migration slowed
down as it expanded, where the migration distance was well fitted by a certain curve proportional to the square
root of the duration, suggesting that the propagation was limited by diffusion with a diffusion coefficient of
about 104 m2 s−1 . This slow slip mechanism differs from nucleation-related pre-slip traditionally applied in
earthquake predictions. The obtained value of the diffusion coefficient is of the same order of magnitude as
that reported for the migration of a deep non-volcanic tremor. These results appear to be compatible with a
conceptual model having strongly coupled patches which, although being separated by decoupled stable regions
on this plate-interface, are not mechanically isolated and which became interactive when they broke.
Key words: Tohoku Earthquake, foreshock, triggering, after-slip, diffusion.
1.
Introduction
The mainshock of the 2011 off the Pacific coast of
Tohoku Earthquake broke the plate interface over almost
500 km (Fig. 1, inset) resulting in a moment magnitude of
Mw 9.0. The sole M 7-class earthquake on the plate interface occurred just before the mainshock, about 1.8 × 105
seconds (51 hours) earlier, about 40 km away up-dip (hereafter, we call this event simply the foreshock). The extent
of the foreshock focal area is thus much constrained by the
spatial distribution of its immediate aftershocks (Fig. 1) and
a seismic inversion (Hayes, 2011). Although any conclusions derived from such different datasets is uncertain, it is
indicated that the rupture was initiated at the southern end
of the source area and the coseismic rupture mainly propagated towards the north. According to a back-projection
analysis, the rupture area of the mainshock was partitioned
from, and did not overlap with, the foreshock area (Kiser
and Ishii, 2011).
Aseismic after-slip is often observed associated with
large earthquakes showing a complementary spatial distribution to coseismic slip areas (e.g., Yagi and Kikuchi, 2003;
Miyazaki et al., 2004). In general, after-slip, aftershocks
and along-fault migrations of large earthquakes have been
described by diffusional processes, which are considered
in relation to fault zone rheology (e.g., Savage, 1971; Ida,
1974) together with contributions from viscous mantle rec The Society of Geomagnetism and Earth, Planetary and Space SciCopyright ences (SGEPSS); The Seismological Society of Japan; The Volcanological Society
of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB.
doi:10.5047/eps.2011.05.016
bound which has an affect for much longer periods: a few
years (e.g., Lehner et al., 1981). More recently, it is proposed that a slow earthquake family may be governed by
diffusion (Ide et al., 2007; Ide, 2010; Ando et al., 2010;
Nakata et al., 2011), with the migration fronts of tremor
and slow slip events (SSEs) following parabolic curves,
T = (1/D)L 2 ,
(1)
where T and L denote the duration and distance of the
migration, respectively, and the constant D is called the
diffusion coefficient presuming underlying diffusional processes. In particular, Ide (2010) found that D ∼ 104 m2
s−1 explained the data well by analyzing tremor migration
beneath western Shikoku for the Nankai subduction zone.
Foreshock-mainshock sequences are also recognized as
earthquake doublets, observed in various tectonic settings,
which phenomenon has been understood in terms of defined
fault segmentations in some form (e.g., Lay and Kanamori,
1980; Engdahl et al., 2007; Nakano et al., 2010). They
serve as a type of earthquake triggering and stress transfer
(King et al., 1994; Gomberg et al., 2001). This context
has particular importance in understanding the current sequence of events, because it has been believed that the plateinterface below the Japan trench contains strongly-coupled
patches that are relatively small, and which define strong
segmentations as impeding gigantic earthquakes (e.g., Lay
and Kanamori, 1981). But, on this occasion, is this view
totally wrong? In this paper, we reexamine it in the light of
the currently observed foreshock-mainshock sequence.
We concentrate on the data analysis for the 2011 Tohoku Earthquake to clarify the seismicity migration pattern
767
768
R. ANDO AND K. IMANISHI: MAINSHOCK TRIGGERED BY FORESHOCK AFTER-SLIP
Fig. 1. Distribution of earthquake events between foreshock and mainshock. (a) Filled circles denote the epicenters of the earthquakes and
their colors represent elapsed time from the foreshock as shown by the
color bar scale. Stars indicate the epicenters of the foreshock and the
mainshock. The red dotted rectangle very roughly encloses the foreshock focal area. Seismicity is sampled for Fig. 2 from two gray dotted
rectangle areas; the colored tick marks inside them represent calculated
rupture front locations at each elapsed time shown by the colors assuming the diffusion coefficient D = 0.78 × 104 (refer to the text for the
detail). (Inset) Mainshock focal area with seismicity from March 9 to
13, 2011 (gray dots). The area enclosed by a red rectangle is magnified.
(b, upper) Map view showing relocated hypocenters (red circles) and
initial hypocenters determined by JMA (black circles). The blue and
black stars are hypocenters of the foreshock and the mainshock, respectively, after and before the relocation. (b, lower) Vertical cross-sectional
view of the upper panel along X–X . Green circles denote hypocenters
in a green rectangle in (b, upper). (c) CMT (Centroid Moment Tensor)
solutions colored with time after the foreshock.
riod between the foreshock and the mainshock. We applied
a bootstrap resampling technique to quantify the precision
of a given location (see Waldhauser and Ellsworth, 2000);
we obtained relative location errors, defined as 1σ , of about
2 km in both horizontal and vertical directions, which is sufficient to discuss the relative locations of the earthquakes
during the migration over nearly 40 km.
We choose hypocenters that can reasonably be assumed
to be on or around the plate interface (Fig. 1(a)). This is
based on the hypocentral depth distribution, which shows a
tendency for the hypocenters to be localized to a plane of
the presumed plate interface which, despite a certain limitation in the accuracy for these offshore events (Fig. 1(b),
lower), is also strongly supported by the CMT solutions,
manually determined by the National Research Institute
for Earth Science and Disaster Prevention (available at
www.fnet.bosai.go.jp), having nodal planes of low-angle reverse faulting (Fig. 1(c)). Note that such features become
more obvious in our targeted area, located between the epicenters of the foreshock and mainshock, than in the case
of further offshore events. The events of JMA magnitude
larger than Mj 1 are included in Figs. 1(a) and (b) but events
larger than Mj 2.6 are involved in the following quantitative analysis. To analyze background seismicity, we used
the JMA earthquake catalog, and earthquakes smaller than
Mj 6 are considered only after January 2000.
Because the propagation of slow slip induces stress perturbation on and around plate interfaces, we can expect the
occurrence of earthquakes that are triggered by slow slip in
the current sequence, as has been observed along the currently targeted subduction zone (e.g., Miyazaki et al., 2004;
Uchida et al., 2004). This situation will also be similar to
the generation of a non-volcanic tremor in association with
slow slip events (SSEs) observed for the various plate interfaces (Rogers and Dragert, 2003; Obara et al., 2004).
Supported by these established observational facts, we can
safely interpret the seismic activity change as the marker of
the propagation of slow slip, i.e., after-slip.
3.
which began at the foreshock and lasted until the mainshock. The background seismicity is also reviewed. An
intuitive understanding of the physical background will be
given by a model having brittle-ductile mixed fault heterogeneity (Ando et al., 2010; Nakata et al., 2011). We will see
below that the seismicity migration follows well the abovementioned parabolic pattern and that the onset timing of the
mainshock corresponds to the arrival of the migration front
to the mainshock hypocentral location.
2.
Method
In order to obtain the seismic activity data, we have applied the double-difference earthquake location algorithm
of Waldhauser and Ellsworth (2000) to routinely determined P- and S-phase arrival time readings from the Japan
Meteorological Agency (JMA). Each event is linked to its
neighbors through commonly observed phases, with the average distance between linked events being 20 km. The data
was obtained from the Japanese nationwide seismic network and the readings by JMA were obtained during the pe-
Results
Figure 1(a) shows the spatio-temporal evolution of seismic activity during the two days between the foreshock and
the mainshock. The colors of the epicenters denote the occurrence time of each earthquake so that we can trace temporal changes in the activity. As seen in the gradual changes
of the colors, the seismicity migrated and expanded from
the focal area of the foreshock, whilst there was an absence of seismicity in some areas. Finally, we can note
that the migration reached the hypocentral location of the
mainshock.
In this migration pattern, the speed of migration appears
to decrease the further it goes. This deceleration might be
related to a diffusional propagation of slow slip as considered in the above-mentioned studies. Therefore, we test
this hypothesis by examining if the migration is explained
by a parabolic curve fitting with a certain diffusion coefficient. For this purpose, we select two representative
cross-sections A–A and B–B indicated by gray rectangles
(Fig. 1(a)), which cover the area inbetween the foreshock
and the mainshock. Because we want to follow how the mi-
R. ANDO AND K. IMANISHI: MAINSHOCK TRIGGERED BY FORESHOCK AFTER-SLIP
Fig. 2. Space-time plots of seismicity in the area between the foreshock
and the mainshock. (a) Red and green open circles denote earthquake
events plotted as functions of the elapsed time and the distance from the
mainshock epicenter along the cross-sections A–A and B–B , respectively (see Fig. 1(a)). Stars indicate hypocenters of the foreshock and
the mainshock. Specification of fitting curves and line are indicated in
the panel. (b) Black circles denote events taken from (a) to define the
migration front and used for the least-squares analysis. Gray parabolic
curves and lines show the resulting least-squares solutions specified in
the inset; thick and thin curves are those from L m = 37 and L m = 32.
gration approaches the mainshock hypocenter, these crosssections are chosen to radiate from this point. Then, we
compare the data with the calculated migration distance L
represented as the function of time T written as
L = (DT )1/2 .
(2)
First, we investigate the migration pattern on the map view
(Fig. 1(a)). The colored tick marks appended inside the gray
rectangles show the locations of the migration fronts at 6
hour intervals calculated from Eq. (2) assuming D = 0.78×
104 m2 s−1 where the color coding corresponds to time after
the foreshock (see color bar scale); these intervals become
closer as time passes following Eq. (2). In this figure, it
is immediately found that the calculated total migration
distance bridges a gap between the foreshock focal area and
the mainshock epicenter, meaning that the given value of D
describes the overall rate of migration well. Comparisons
between the colors of the ticks and the epicenters enable
a more detailed investigation into the migration process.
(Note that we need to trace the front of the migration, which
corresponds to the first event at a certain location, whereas
some events can be obscured by neighboring later events on
this figure.) Although the event locations are spotty, we can
see that the overall pattern of their gradual color changes
is also well correlated with the tick colors. In particular, it
769
is clearly seen that the migration front extended more than
half the total distance during the first half a day, and took
another 1.5 days to extend the remaining distance.
Next, in Fig. 2, we will detail the migration pattern on
a space-time plot, which enables a more precise comparison of observation with theory. The occurrence time of
the earthquakes included in the cross-sections A–A and B–
B are plotted as a function of the epicentral distances. By
observing Fig. 2(a), it is confirmed that the seismicity actually migrates from the foreshock focal area and then gradually approaches the mainshock hypocenter. Aside from
the migration, the continuing activity around the foreshock
hypocenter must be attributable to its aftershocks in the
usual sense. Plotting Eq. (1) with D = 0.78 × 104 placed
the origin at the foreshock hypocenter, L m ∼ 37, which actually is one of the least-squares solutions of the parabolic
fitting described below, and we can see that the curve describes the trend of the migration front originating from
there. Whilst the sole outlier is found near L m = 20 for the
cross-section B–B and occurred within 2000 s, this might
be triggered by coseismic stress changes rather than a propagating slow slip, since this location appears to be susceptible to a small stress observing the continuing activity resulted in a cluster (see also Fig. 1). Note that we do not
attempt to discuss precisely the values of D, however, it is
obvious that the values are in a range of an order of magnitude since D = 103 and 105 do not fit the data at all.
Finally, we quantitatively evaluate the other possibilities:
(1) linear function fitting and (2) a different migration start
point assumed at L m = 32 as an extreme case considering
an extraordinarily larger foreshock focal area. Figure 2(b)
shows the used dataset and the obtained least-squares solutions with the root mean squares of the sum of their squared
residuals. In order that the dataset on the migration is kept
as simple as possible, we eliminated only the obvious aftershocks and the above-mentioned continual activity, so
as not to be biased too much by these different phenomena. As a result, we can see that the linear function fittings have larger residuals than the parabolic cases for both
assumed starting points (Removing a tricky data point at
L m = 26 changes the residual by less than 10%, and does
not change this tendency.) Moreover, we find that the linear
cases cannot follow the overall trend if one attempts to explain reasonably all the data points from the foreshock area,
L m ∼ 37, to the mainshock hypocenter, L m = 0, through
the recognizable migration front between L m ∼ 5–20 (the
reason for the lack of seismicity inbetween is discussed below). These fitting results are basically valid even allowing
for possible epicentral determination errors.
4.
Discussions and Conclusion
Here, we will overview the seismic background of this region (Fig. 3). This region is rich in seismic activity often becoming M 5-class but occasionally M 7-class. As shown in
Fig. 3(a), such relatively large events appear to be concentrated on the western, down-dip, half of this region, overlapped with clouds of background seismicity. There was
a sequence in January 1981 involving events of Mj 6.0–7.0
in and around the focal area of the current foreshock. In
Fig. 3(b), it is also shown that the foreshock area extends
770
R. ANDO AND K. IMANISHI: MAINSHOCK TRIGGERED BY FORESHOCK AFTER-SLIP
Fig. 4. Schematic diagram showing an earthquake sequence on the plate
interface from the foreshock to the mainshock. White stars illustrate
hypocenters. Weak planes located around the plate interface (not shown
here) can be ruptured during the sequence.
Fig. 3. Spatial distribution of background seismicity. (a) Filled circles
denote events larger than Mj 6 which occurred from 1967 to 2010 (see
inset for magnitudes and origin times, respectively, depicted by sizes
and colors). Open red circles denote seismicity in the current foreshock-mainshock sequence. Gray dots denote the seismicities of the
background in the time and depth ranges of January 2000—September
2010 and 1–50 km, respectively. Blue stars denote epicenters of the
current foreshock and mainshock, and the 2005, Mj 6.3, event as indicated in (b). (b) Green dots denote seismicity activated in August 2005.
(c) Space-time plot of seismic sequence of 1981 along the rectangular
cross-section C–C shown in (a).
over a cluster, which was activated with Mj 6.3, on August
24, 2005. In addition, the after-slip-induced activities (see
Figs. 1 and 3) overlap with obvious clusters observed in the
background seismicity. It is important to point out that the
focal areas of the current events obviously correlate with
these previous focal areas which suggests the existence of
persistent fault structures, but the rupture processes are not
just repetitions having the same form.
In Fig. 2, we saw an area with an apparent lack of seismicity for L m ∼ 20–35. This apparent deficit seems to be
characteristic of this area as exemplified by long-term seismic activity (Fig. 3). We can, perhaps, suppose both decoupling and coupling just to interpret this seismic gap but the
slow propagation of the after-slip through the gap is incom-
patible with the latter because, if such a large coupled patch
breaks, the rupture would be accelerated to be a standard
earthquake. Therefore we can presume that this area is persistently decoupled as indicated in Fig. 3(b). In this respect,
the seismic sequence in January, 1981, provides an interesting perspective because, beyond this gap, the onset of the
M 6.6 events on January 23 was largely delayed after the
M 7.0 event on January 19. In fact, it suggests that the delay
can be explained by a parabolic curve with D = 0.46 × 104
(Fig. 3(c)), which is the same, by an order of magnitude, as
that for the current foreshock-mainshock sequence.
Although detailed physical interpretations are beyond the
focus of this paper, it might be worth providing an illustration of possible rupture mechanisms and fault properties
underlying this observed sequence (Fig. 4). It is considered
that the foreshock broke through strongly-coupled neighboring patches existing on an otherwise decoupled background. The rupture initiated near the rim of a patch probably due to stress concentration by steady sliding on the
surrounding stable area. The background is stable with a
fault property exhibiting velocity strengthening, so that the
raised stress along the perimeter of the broken area starts to
slowly diffuse with after-slip; the velocity strengthening is
essential to interpret the slow after-slip otherwise the afterslip ceases immediately transferred by a seismic wave. Distributed small coupled patches were overrun in the afterslip propagation and ruptured seismically, resulting in signals which indicated the location of the propagation front.
The after-slip finally reached the location of the mainshock
hypocenter and triggered the dynamic rupture there, presumably involving multiple patches. The active production
and partitioned slip distribution of major (M ≥ 7) interplate aftershocks (Kiser and Ishii, 2011) suggest the existence of such a heterogeneous fault structure. On the other
hand, the after-slip alone could not have caused the gigantic
earthquake because the stress perturbation accompanying
R. ANDO AND K. IMANISHI: MAINSHOCK TRIGGERED BY FORESHOCK AFTER-SLIP
the after-slip did not have such a large reach, therefore it
has to be considered that the coupled patches in the mainshock focal area were tectonically pre-stressed and susceptible to triggering by the after-slip and to sustaining the rupture propagation. Either way, the after-slip of the foreshock
probably played a role of giving the last push.
The above view is qualitatively supported by physicsbased simulations (Ando et al., 2010; Nakata et al., 2011)
demonstrating that, if a number of coupled patches almost
equally reach their critical stress state, these patches can be
ruptured in a sequence even though the patches are sparsely
distributed to some extent. We speculate that such a synchronization, which rarely occurs over a great distance,
might have happened this time. The simulations further
clarify that the degree of the patch interactions is controlled
by the patch distributions, and that the parabolic and diffusional slow slip propagation occurs under a certain rheological fault condition.
The existence of a strict control in after-slip propagation (Eq. (2)) and the possibility of signal detection offer
a chance to predict the occurrence of subsequent earthquakes in the preceding hours or days, although we may
always expect fluctuations depending on conditions. However, because this phenomenon alone cannot alert us to
earthquake generation, in order to accomplish such a prediction we need to know beforehand the locations of coupled patches and their tectonic stress levels. Such evaluations could be made possible by improvements in geodetic (e.g., Hashimoto et al., 2009) and seismic (e.g., Uchida
et al., 2004) monitoring for plate coupling, combined with
paleo-seismological history reconstruction (e.g., Sawai et
al., 2009) to quantify elapsed times since previous earthquakes and their magnitudes. It is also essential to develop proper physical fault models to input these data and
to translate them into physical fault states. Since the degree of plate-coupling has localities (Lay and Kanamori,
1981) and the interactive behaviors between fault segments
(or patches) are not straightforward, a physics-based understanding is important to compensate for our limited experiences. Earthquake studies following such a direction
could be applied to consider other potentially catastrophic
earthquakes, such as that on the Nankai subduction zone off
southwest Japan.
Acknowledgments. Suggestions by Y. Yoshida improved the
manuscript. We are grateful to the Japan Meteorological Agency
(JMA) for the P- and S-phase arrival time readings and the earthquake catalog. The data was processed in collaboration with the
JMA and the Ministry of Education, Culture, Sports, Science
and Technology (MEXT). This work was partially supported by
MEXT KAKENHI (21107007).
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